The most common and most likely answer to this crossword clue is the 5 plus 3 letter word PRESS UPS
I've seen this crossword clue in Financial Times
P
R
E
S
S
U
P
S
Buddy explains!
The straight part
We know that "Army exercises" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case army exercises = press ups.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does PRESS UPS mean?
PRESS UPS noun- An exercise done to improve upper body strength, performed by resting on one's toes and hands and pushing one's weight off the floor.
- A push-up bra.